AP State Syllabus AP Board 9th Class Maths Solutions Chapter 6 Linear Equation in Two Variables InText Questions and Answers.

## AP State Syllabus 9th Class Maths Solutions 6th Lesson Linear Equation in Two Variables InText Questions

**Try This**

Question 1.

Express the following linear equations in the form of ax + by + c = 0 and indicate the value of a, b, c in each case. [Page No. 128]

i) 3x + 2y = 9

Solution:

3x + 2y = 9

⇒ 3x + 2y – 9 = 0

Here a = 3, b = 2, c = -9

ii) – 2x + 3y = 6

Solution:

– 2x + 3y = 6

⇒ – 2x + 3y – 6 = 0

Here a = -2, b = 3, c = -6

iii) 9x – 5y = 10

Solution:

9x- 5y = 10

⇒ 9x- 5y – 10 = 0

Here a = 9, b = -5, c = -10

iv) \(\frac{x}{2}-\frac{y}{3}-5=0\)

⇒ \(\frac{3 x-2 y-30}{6}=0\)

⇒ 3x – 2y – 30 = 0

Here a = 3, b = – 2 and c = – 30

v) 2x = y

Solution:

2x = y

⇒ 2x – y = 0

Here a = 2, b = – 1 and c = 0

**Try These**

Take a graph paper, plot the point (2, 4), and draw a line passing through it. Now answer the following questions. [Page No. 135]

Question 1.

Can you draw another line that passes through the point (2, 4) ?

Solution:

Yes, We can draw another line passing through (2, 4).

Question 2.

How many such lines can be drawn ?

Solution:

Infinitely many lines can be drawn.

Question 3.

How many linear equations in two variables exist for which (2, 4) is a solution ? Solution:

Infinitely many linear equations in two variables exist.

Graph is given in next page.

**Do This**

Question 1.

i) Draw the graph of following equations. [Page No. 145]

a) x = 2 b) x = -2 c) x = 4 d) x = -4

ii) Are the graphs of all these equations parallel to Y-axis? .

Solution:

Yes; all these lines are parallel to Y-axis.

iii) Find the distance between the graph and the Y-axis in each case.

Solution:

Graph | DIstance | Right side/left side of the origin |

a) x = 2 | 2 units | Right side |

b) x = -2 | 2 units | Left side |

c) x = 4 | 4 units | Right side |

d) x = -4 | 4 units | Left side |

Question 2.

i) Draw the graph of the following equations. [Page No. 145]

a) y = 2 b) y = -2 c) y = 3 d) y = – 3

Solution:

ii) Are all these parallel to the X-axis?

Solution:

Yes, these are all parallel to X-axis.

iii) Find the distance between the graph and the X-axis in each case.

Graph | DIstance | side of the origin above/below |

a) y = 2 | 2 units | above origin |

b) y = -2 | 2 units | below origin |

c) y = 3 | 3 units | above origin |

d) y = -3 | 3 units | below origin |

**Try These**

Question

Find the equation of the Y – axis. [Page No. 146]

Solution:

All points on Y – axis have their x – co-ordinates as zero.

∴ Equation of Y- axis is x = O.